Optimal Right Restricted Multiplicative Schwarz Preconditioning for the Flux-Limited Multi-Group Radiation Diffusion Equations in Three Dimensions

The present article is concerned with optimal exact and inexact right restricted multiplicative Schwarz preconditioning algorithms for flux-limited multi-group radiation diffusion equations in three dimensions. We give their effective constructions and establish the field-of-values equivalence analyses. They are applied to the restarted generalized minimal residual solution strategies to iteratively search numerical approximations within the associated Krylov subspace. Sequential and two-layer hierarchical parallel experimental evidences on the realistic unstructured coupled hydrodynamic instabilities during the inertial confinement fusion capsule implosion deceleration phase are provided. Numerical results on the Tianhe-Xingyi supercomputer reveal the superior performance of our proposed preconditioning approaches over several existing popular monolithic and block preconditioning techniques.